The answer is positive. For any Jordan curve, there is a homeomorphism of the Riemann sphere, which sends this curve to a circle. Your statement immediately follows.

One prove of this statement involves the Riemann mapping theorem and the boundary correspondence theorem of Caratheodory. But there are also pure topological proofs, of course.

The answer is positive. For any Jordan curve, there is a homeomorphism of the Riemann sphere, which sends this curve to a circle. Your statement immediately follows.

One proof of this statement involves the Riemann mapping theorem and the boundary correspondence theorem of Caratheodory. But there are also purely topological proofs, of course.